Alright, let's solve this problem step by step. We have 5025 and 6154 and we're adding them together.

Step 1: We'll start by adding the digits 5 & 4 in column 1 and get 9.

Step 2: We'll start by adding the digits 2 & 5 in column 2 and get 7.

Step 3: We'll start by adding the digits 0 & 1 in column 3 and get 1.

Step 4: We'll start by adding the digits 5 & 6 in column 4 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

So, 5025 + 6154 = 11179.

